A flat coil of wire, consisting of 30 circular loops with a total resistance of

Question

A flat coil of wire, consisting of 30 circular loops with a total resistance of 20.0 , is placed so that it is at rest, flat on a table. The graphs below show the magnetic flux through each loop of the coil as a function of time, for three different cases. The units of flux are webers, which are equivalent to tesla meters2. The flux through each loop changes because the magnetic field changes. Assume that the field is uniform and the direction of the field is perpendicular to the plane of the coil-positive flux means the field is passing in one direction through the coil, and negative flux means that the field is passing through the coil in the opposite direction. (T m2) 0.40 0.20 0(T m2) 0.40 0.20 t (s) 10 15 2025 5 10 15 2025 0.20 -0.40 0.20 -0.40 0(Tm2) 0.40 t (s) 5 10 15 20 25 0.20 -0.40 (a) Rank the cases based on the magnitude of the flux passing through each loop of the coil at a time of t not include any parentheses around the letters or symbols.) 23 s, from largest to smallest. (Use only">" orsymbols. Do (b) Rank the cases based on the magnitude of the induced current in the coil at a time of t23 s, from largest to smallest. (Use only">orsymbols. Do not include any parentheses around the letters or symbols.) (c) In case C, calculate the magnitude of the induced current in the loop at t = 7 s. (d) In case C, calculate the magnitude of the induced current in the loop at t 17.5 s

Explanation / Answer

Solution:

a) We can see from the graph as We are considering magnitude the order should be

=> C > A > B

b) Now induced current is directly proportional to induced emf, so if induced emf is more incuded current will be more so the question boiled down to rank according to induced emf , Induced emf is given by the slope of the flux and time graph, (Note: As mentioned in question we will not consider sign here, we only need magnitude)

At t = 23 s , Slope of A = slope of B , and Slope of C = 0 , Hence Ranking is

=> A = B > C

c) As stated in question b slope of flux time graph will give induced emf. So induced emf at t = 7 s

slope of C at t = 7 = (0.20-0)/(15-5) = 0.02 V

induced current(i) = (emf / R) * N

=> i = (0.02 / 20) * 30 = 0.001 * 30 A

=> i = 0.001 x 30 = 0.03 A

d) Slope of the graph at t = 17.5 sec

=> e = (-0.20-0.20)/20-15

=> e = 0.08 V (taking only magnitude neglecting sign)

induced current (i)

=> i = (e / R) * N

=> i = (0.08/20) * 30

=> i = 0.004 * 30 A

=> i = 0.12 A

e) Given induced current is directed clockwise induced current will be directed clockwise if sign of the slope is same as when t = 12 s in A

so,

i) t = 17 s in A

ii) t = 6 s in B

(iii) t = 22 s in B

(iv) t = 3 s in C

(v) t = 17 s in C

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